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Bifurcation of non-negative solutions for an elliptic system

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Applied Mathematics and Mechanics(English Edition) 2008年第2期29卷 251-257页

作者：杨明石佩虎 Department of Mathematics Southeast University

In the paper, we consider a nonlinear elliptic system coming from the predator-prey model with diffusion. Predator growth-rate is treated as bifurcation parameter. The range of parameter is found for which there exist... 详细信息

关键词： bifurcation structure of positive solutions elliptic system

Existence of Solutions for the Critical elliptic system with Inverse Square Potentials

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 315-328页

作者： Zhao-xia LIU Zhao-hui LIU Department of Information and Computational Science School of Sciences Minzu University of China Suncun Middle School Gaoxin District of Jinan

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s... 详细信息

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s）. Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.

关键词： elliptic system variational functional Palais-Smale condition critical point

Positive Solutions to a Neumann Problem of Semilinear elliptic system with Critical Nonlinearity

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Acta Mathematicae Applicatae Sinica 2006年第4期22卷 687-702页

作者： Wei-hua Yang Academy of Mathematics and systems Science Chinese Academy of Science Beijing 100080 China

In this paper, we consider the Neumann boundary value problem for a system of two elliptic equations involving the critical Sobolev exponents. By means of blowing-up method, we obtain behavior of positives with low en... 详细信息

关键词： elliptic system Neumann problem critical Sobolev exponent

MULTIPLICITY OF POSITIVE SOLUTIONS FOR AN elliptic system

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Analysis in Theory and Applications 2003年第2期19卷 145-152页

作者： Han Zhaoxiu (ZheJiang University, China)Department of Mathematics Zhejiang University Hangzhou,Zhejiang,310028 P.R.China Department of Mathematics Zhejiang University Hangzhou Zhejiang P. R. China

By considering the properties of , we show the multiplicity of at least two positivesolutions of the elliptic system.

关键词： multiplicity elliptic system

Positive Entire Solutions to an elliptic system

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Northeastern Mathematical Journal 2001年第1期17卷 1-4页

作者：张中新王俊禹黄明游 InstituteofMathematics JilinUniversityChangchun130021 不详

In a recent paper [1], Ye has demonstrated that the singular nonlinear elliptic equation has a positive entire solution under some conditions imposed on f. Problems of finding positive entire solutions to elliptic equations have been studied by many authors since they have certain physical backgrounds and practical applications. For details, see, for example, [ 1-3] and the references therein.

关键词： elliptic system positive entire solution existence

MULTIPLE SOLUTIONS OF SOME elliptic systemS WITH LINEAR COUPLINGS

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Acta Mathematica Scientia 2021年第4期41卷 1141-1150页

作者： Yutong CHEN Jiabao SU Mingzheng SUN Rushun TTAN School of Mathematical Sciences Capital Normal UniversityBeijing 100048China College of Sciences North China University of TechnologyBeijing 100144China

In this paper,we study the existence of nontrivial solutions to the elliptic system {-△u=λv+Fu(x,u,v),x∈Ω,-△v=λu+Fv(x,u,v),x∈Ω,u=v=0,x∈∂Ω,where Ω■R^(N) is bounded with a smooth *** the Morse theory and the... 详细信息

关键词： Morse theory multiplicity elliptic system linear couplings

ON THE NONLINEAR RIEMANN PROBLEMS FOR GENERALFIRST elliptic systemS IN THE PLANE

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Applied Mathematics and Mechanics(English Edition) 2005年第1期26卷 79-84页

作者：李明忠宋洁 Department of Mathematics Shanghai University Shanghai 200444 P.R.China Department of Mathematics East China University of Science and TechnologyShanghai 200237 P.R.China

The nonlinear Riemann problem for general systems of the first-order linear and quasi-linear equations in the plane are *** translates them to singular integral equations and proves the existence of the solution by me... 详细信息

关键词： Riemann problem elliptic system singular integral equation

A Note on Solutions for Asymptotically Linear elliptic systems

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 511-522页

作者： Lei-ga Zhao Department of Mathematics Beijing University of Chemical Technology 100029 Beijing China Academy of Mathematics and systems Science Chinese Academy of Sciences Beijing 100190 China Department of Mathematics Yunnan Normal University Kunming 650092 China

In this paper, we are concerned with the elliptic system of{ -△u＋V（x）u=g（x,v）, x∈R^N, -△v＋V（x）v=f（x,u）, x∈R^N, where V（x） is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods.

关键词： elliptic system ground state solution variational methods concentration-compactness principle

EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR elliptic systemS IN R^N WITH ZERO MASS

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Acta Mathematica Scientia 2013年第4期33卷 913-928页

作者：李工宝叶红雨 School of Mathematics and Statistics Central China Normal University

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.

关键词： existence positive solutions elliptic system linking geometric structure zero mass case